Stir together water and corn syrup in a small saucepan; bring just to a boil over medium-high heat. With the food processor running, add the syrup mixture, then vanilla. Continue processing until the sauce is smooth, scraping down the sides as needed. (The sauce will seem thin, but will thicken during cooling.) Transfer to a container and refrigerate until chilled, at least 2 hours. Stir well before serving; if the sauce seems too thick, stir in a little water.